The pair have entered the final 10 months of their contacts at Stamford Bridge and the club are keen for them to sign on.
As Sunsport exclusively revealed, Christensen, 25, is expected to sign a new long-term contract worth £120,000.
French World Cup winner N’Golo Kante and Euros champion Jorginho have 24 months left on their current deals and are expected to be handed new contracts by the club.
Academy graduate Mason Mount has impressed since being given his debut by former boss Frank Lampard and has become a key man for club and country.
And the England international, 22, is expected to become one of the top earners at the club after his stellar performances.
But as Mount is a fan of the club and recently signed a new deal in 2019 – Christensen and Rudiger are Chelsea’s priority.
Alongside Rudiger and Thiago Silva, Dane Christensen has excelled in Tuchel’s preferred 3-4-3 formation.
He played a key role in winning the Champions League last season and is a key part of the club’s future while the German remains as boss.
But Rudiger, 28, has stalled on signing a new deal after it was reported he was open to leaving for free next summer.
The former Roma centre-back is believed to want around £200,00-a-week and has interest from both Paris Saint-Germain and Real Madrid.
And Tuchel even admitted talks had hit an impasse.
He said: “I hope that they find solutions, but it’s not only between coaches and players, and what we wish for.
“And that’s why it’s between the club and the player’s agent at the moment.
“He’s in the strongest league in Europe, in a big club, so not many reasons to change that. But in the end, it’s between him and the club, and that’s in good hands.”
Blues skipper Cesar Azpilicueta is also in the final year of his contract but he and the club are not worried about signing a new deal.